In the case of a Tier 2 offering, issuers must provide audited financial statements for their prior two years (a one - year old company files a one year audit) in the offering statement and annual reports.
All filings with the SEC have to be prepared in accordance with GAAP, and Reg A Tier 2 requires an audit opinion.
The SEC will be looking for statements like this in the audit opinion; "The consolidated financial statements referred to above present fairly, in all material respects, the financial position of Example Company as of December 31, 20xx, and 20xx + 1, and the results of their operations and their cash flows for the years then ended in accordance with accounting principles generally accepted in the United States."
The most likely consequence of filing non-GAAP financial statements is that the filing will be bounced immediately, with the filer being told that no review is possible until correct financial statements are produced.